# Research

I am currently working with David Aristoff and Olivier Pinaud. We study convergence rates and spectral properties of Bayesian sampling algorithms and Markov processes.

My recent publication with David Herzog, Gabriel Stoltz, and Maria Gordina establishes explicit rates of convergence for Langevin dynamics subject to singular potentials in a weighted norm.

More recently, with David Herzog, we have proven on the asymptotic behavior of degenerately stochastically forced Lorenz 96 systems.

My mathematical research and interests lie in:

Stochastic Processes

Chaos Theory and Nonlinear Dynamics

Functional Analysis

Partial Differential Equations

Quantum Mechanics

Mathematical Chemistry

## A recent presentation of our Langevin dynamics results.

# Research with Undergraduates

I was privileged enough to participate in mathematics research as an undergraduate at Concordia College, as well as through an NSF-funded research program at New York University. These experiences were invaluable to my future career as a mathematician, and I try to participate in leading undergraduate research whenever possible. The list of program topics I have led with undergraduates includes:

Fractals and iterated function systems

Sampling and interpolation theory

Markov chains and mixing times

Models for turbulent flow

Semigroup theory

Fractional operator theory

Selected Publications:

Weighted L2-contractivity of Langevin dynamics with singular potentials

Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]

Stability of the Kaczmarz reconstruction for stationary sequences

On the nature of the conformable derivative and its applications to physics

A tractable numerical model for exploring nonadiabatic quantum dynamics

Links to my research profiles: